Problem: Simplify the following expression: $ z = \dfrac{5x}{10x - 2} + \dfrac{2}{7} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{5x}{10x - 2} \times \dfrac{7}{7} = \dfrac{35x}{70x - 14} $ Multiply the second expression by $\dfrac{10x - 2}{10x - 2}$ $ \dfrac{2}{7} \times \dfrac{10x - 2}{10x - 2} = \dfrac{20x - 4}{70x - 14} $ Therefore $ z = \dfrac{35x}{70x - 14} + \dfrac{20x - 4}{70x - 14} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{35x + 20x - 4}{70x - 14} $ $z = \dfrac{55x - 4}{70x - 14}$